Micromechanically-motivated phase field approach to ductile fracture

Abstract

Utilization of the phase-field diffusive crack approach in prediction of crack evolution in materials containing voids is investigated herein. It has been established that the ductile failure occurs predominantly due to nucleation, growth and coalescence of micro-voids and micro-cavities, which lead to initiation and propagation of cracks till final material collapse. This study is an attempt to model the material internal degradation with the Rousselier pressure-dependent plasticity law, assisted with the phase field diffusive crack approach for the first time, in order to account for the post-critical softening regime. Such treatment requires the utilization of a damage evolution law and a crack initiation criterion which triggers the succeeding crack propagation, whereby a modified crack driving force based on the sequence of internal damage is employed. In numerical terms, the proposed model is integrated within a fully-staggered framework for the mechanical and diffusive fields and is implemented via the finite element method. The verification tests on the model is processed by several examples with the focus on both qualitative monitoring of pathological crack patterns and the quantitative analysis on the material response, particularly in the post-critical range, complemented by relevant comparisons with the existing data from literature.

Assessment of four strain energy decomposition methods for phase field fracture models using quasi-static and dynamic benchmark cases

“…Wu (2017) built a unified phase field fracture model for static and quasi-static fracture problems by including multiple degradation functions. Phase field fracture models have been applied in many areas, including cohesive zone modeling (Verhoosel and de Borst 2013;May et al 2015;Nguyen and Wu 2018), ductile fracture (Ambati et al 2015b;Ambati et al 2016;Dittmann et al 2018;Azinpour et al 2021), hydraulic fracture (Miehe and Mauthe 2016;Wilson and Landis 2016;Heider and Markert 2017;Zhuang et al 2020;Heider et al 2018), and thermomechanical fracture (Kuhn and Müller 2009;Nguyen et al 2019;Svolos et al 2020;Rezwan et al 2021). Phase field fracture methods have also been expanded to model dynamic fracture (Karma et al 2001;Bourdin et al 2011;Larsen 2010), with the most widely used approach developed by Borden et al (2012).…”

Revisiting the fracture forming limits of bulk forming under biaxial tension

“…Microstructure-based coupled ductile damage models (e.g., Tvergaard and Needleman, 1984, or Azinpour et al., 2021) and macromechanics-based coupled models (e.g., Kachanov, 1958; Keshavarz and Ghajar, 2019; Lemaitre, 1985) will be left out of this discussion because despite their merits in adjusting the stress response of the materials as a function of the accumulated damage they do not have an explicit direct link to the three different crack opening modes of fracture mechanics. Moreover, they are more difficult to calibrate due to the relatively large number of parameters involved and have an algebraic treatment that is very difficult or even impossible to be handled within the objectives of this paper.…”

Numerical simulation on hydraulic fracture propagation in laminated shale based on thermo-hydro-mechanical-damage coupling model

“…The results show that there are five fundamental initiation and propagation modes of HFs along the vertical direction of the bedding plane, and the final fracture geometry shape can be divided into four types: simple fracture, fishbone-like fracture, fishbone-like fracture with open fracture and multilateral fishbone-like fracture network. Due to the limitation of the laboratory scale, quantitative analysis is difficult to conduct, so many scholars carry out hydraulic fracturing research employing numerical simulations, including some methods based on the continuum model, such as the finite element method (FEM), extended finite element method (XFEM), boundary element method (BEM) and displacement discontinuity method (DDM), and some methods based on the discontinuous models such as the discrete element method (DEM) and phase-field method (PFM) developed in recent years (Sun and Xu 2022;Zhao et al, 2017;Zou et al, 2017;Azinpour et al, 2021;Zeng et al, 2019;Jamaloei 2021). Based on a previously developed two-dimensional RFPA model, Li et al (2012) established a three-dimensional finite element model considering seepage, damage and stress fields to simulate hydraulic fracturing.…”